Alternating directions parallel hybrid memory iGRM direct solver for non-stationary simulations

Authors

DOI:

https://doi.org/10.7494/csci.2020.21.4.3834

Keywords:

isogeometric finite element method, integration, shared memory, parallel

Abstract

The three-dimensional isogeometric analysis (IGA-FEM) is a modern method for simulation. The idea is to utilize B-splines or NURBS basis functions for both computational domain descriptions and the engineering computations. Refined isogeometric analysis (rIGA) employs a mixture of patches of elements with B-spline basis functions, and $C^0$ separators between them. It enables a reduction of the computational cost of direct solvers. Both IGA and rIGA come with challenging sparse matrix structure, that is expensive to generate. In this paper, we show a hybrid parallelization method to reduce the computational cost of the integration phase using hybrid-memory parallel machines. The two-level parallelization includes the partitioning of the computational mesh into sub-domains on the first level (MPI), and loop parallelization on the second level (OpenMP). We show that hybrid parallelization of the integration reduces the contribution of this phase significantly. Thus, alternative algorithms for fast isogeometric integration are not necessary.

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Author Biographies

Maciej Woźniak, AGH University of Science and Technology

Maciej Wozniak is post-doc at the Department of Computer Science at AGH University, Krakow, Poland.
His research interests include optimization of solver algorithms for different architectures of parallel
machines, isogeometric analysis as well as tree algorithms.

Anna Janina Bukowska, AGH University of Science and Technology

Anna Bukowska is a masters degree student of Computer Science at AGH University, Krakow, Poland.
Her research interests include concurrency theory, isogeometric analysis and adaptive algorithms.

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Published

2020-11-03

How to Cite

Woźniak, M., & Bukowska, A. J. (2020). Alternating directions parallel hybrid memory iGRM direct solver for non-stationary simulations. Computer Science, 21(4). https://doi.org/10.7494/csci.2020.21.4.3834

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